# Momentum thickness

In

aeronautics andviscous fluid theory , the**boundary layer thickness**($\{delta\}$) is the distance from a fixed boundary wall where zero flow is considered to occur, and beyond $\{delta\}$ the fluid is considered to move at a constant velocity. This distance is calculated based on the total momentum of the fluid, rather than the total mass, as in the case ofdisplacement thickness ($\{delta^*\}$). The region of moving fluid contains a percentage (typically 97%) of the fluid's momentum, leading to the definition (fromincompressible fluid theory and thecontinuity equation ) mathematically, of::$\{delta^*\}=\; int\_0^delta\; \{(1-\{uover\; u\_0\})dy\}$

The

**momentum thickness**,**θ**, is a theoretical length scale to quantify the effects of fluidviscosity in the vicinity of a physical boundary. Mathematically it is defined as:$heta\; =\; int\_0^infty$u(z)over u_o} {left [1 - {u(z)over u_o} ight] dz

**(2.1)**where the vertical coordinate, z, is increasing upward from the boundary and u

_{o}is the velocity in theideal flow of the free stream. Thevelocity in a frictionalboundary layer is subject to theno-slip boundary condition at the surface (z = 0) and asymptotically approaches the free stream value (u_{o}). Compared topotential flow , this would be the distance that the surface would be displaced for the flow to have the same momentum. The influence of fluidviscosity creates a wallshear stress , $au\_w$, which extracts energy from the mean flow. The boundary layer can be considered to possess a total momentum flux deficit,:$ho\; int\_0^infty\; \{u(z)\; [u\_o\; -\; u(z)]\; \}\; dz$

**(2.2)**due to the frictional

dissipation . It may also be designated as δ_{2}as in Schlicting, H. (1979)*Boundary-Layer Theory*McGraw Hill, New York, U.S.A. 817 pp.For a flat plate at no

angle of attack with a laminar boundary layer, the Blasius solution gives:$heta\; =\; 0.664\; sqrt$ u x}over u_o}

**(2.3)**Other length scales describing viscous boundary layers include the

boundary-layer thickness , $delta$,displacement thickness , $delta^*$, andenergy thickness , $delta\_3$.

*Wikimedia Foundation.
2010.*

### Look at other dictionaries:

**Momentum exchange tether**— Momentum Exchange Tethers is one of many applications for space tethers. This sub set represents an entire area of research using a spinning conductive and/or non conductive tether to throw spacecraft up or down in orbit (like a sling), thereby… … Wikipedia**Boundary-layer thickness**— This page describes some parameters used to measure the properties of boundary layers. Consider a stationary body with a turbulent flow moving around it, like the semi infinite flat plate with air flowing over the top of the plate. At the solid… … Wikipedia**Audio tape length and thickness**— Since the widespread adoption of reel to reel audio tape recording in the 1950s, audio tapes and tape cassettes have been available in many formats. This article describes the length, tape thickness and playing times of some of the most common… … Wikipedia**Shape factor (boundary layer flow)**— A shape factor is used in boundary layer flow to determine the nature of the flow.:H= frac {delta^*}{ heta}where H is the shape factor, delta^* is the displacement thickness and θ is the momentum thickness. Displacement thickness is defined as… … Wikipedia**Dimensionless quantity**— In dimensional analysis, a dimensionless quantity or quantity of dimension one is a quantity without an associated physical dimension. It is thus a pure number, and as such always has a dimension of 1.[1] Dimensionless quantities are widely used… … Wikipedia**Görtler vortices**— In fluid dynamics, Görtler vortices are secondary flows that appears in a boundary layer flow along a concave wall. If the boundary layer is thin compared to the radius of curvature of the wall, the pressure remains constant across the boundary… … Wikipedia**толщина потери импульса**— (δ**) Величина, которая характеризует изменение количества движения массы газа, протекающей через рассматриваемое сечение пограничного слоя, вследствие действия сил трения. Примечание Уравнение для расчета толщины потери импульса получается … Справочник технического переводчика**radioactivity**— /ray dee oh ak tiv i tee/, n. Physics, Chem. the phenomenon, exhibited by and being a property of certain elements, of spontaneously emitting radiation resulting from changes in the nuclei of atoms of the element. Also called activity. [1895… … Universalium**solids, mechanics of**— ▪ physics Introduction science concerned with the stressing (stress), deformation (deformation and flow), and failure of solid materials and structures. What, then, is a solid? Any material, fluid or solid, can support normal forces.… … Universalium**Business and Industry Review**— ▪ 1999 Introduction Overview Annual Average Rates of Growth of Manufacturing Output, 1980 97, Table Pattern of Output, 1994 97, Table Index Numbers of Production, Employment, and Productivity in Manufacturing Industries, Table (For Annual… … Universalium